Harvesting offshore wind energy conventionally relies on multi-megawatt direct-drive permanent-magnet synchronous generators equipped with full-power-rated active rectifiers. Functional integration of the generator and rectifier has led to the creation of an integrated generator-rectifier system with higher efficiency, reliability and power density. In this architecture, power electronics weight and efficiency depend on the generator inductance, while at the same time, the generator design must be optimized for weight and efficiency to realize the potential system-level benefits. This paper proposes a framework using the generator per-unit reactance as a handshake variable to co-design the generator and power electronics. The design approach enables the reduction of the system weight and conversion losses by 25% and 61%, respectively, for a 10-MW system. Using conservative assumptions, economic and reliability assessments show a 4.5% increase in annual energy production, a 9x reduction in long-term failure rate, and a 6.5% decrease in levelized cost of electricity.